In the book on information theory entitled "Information Theory and Reliable Communication", authored by R. G. Gallager and published by John Wiley, 1968, Gallager shows how the capacity of a time-continuous channel with intersymbol interference and colored noise may be determined. The time-continuous channel of interest is shown in FIG. 1 wherein: channel 100 has impulse response h(t); the input time signal 101 to channel 100 is s(t); one component of the output signal 103 of channel 100 is signal 102 given by s.sub.o (t) (with s.sub.o (t) being the convolution of s(t) and h(t)); and the other component of output signal 103 is additive noise 104 represented by n(t). Both components of output signal 103 are combined in summer 105. As shown in FIG. 2, which includes the frequency domain equivalent of FIG. 1, the first step disclosed by Gallager was that of filtering the channel output 103 with equalizer 201 to flatten the noise spectrum; equalizer 201 has a transfer function given by [N(.omega.)].sup.-1/2, where N(.omega.) is the spectrum of the noise. With reference to FIG. 3, the white noise model equivalent to FIG. 2 is shown wherein: the equivalent channel 301 is the original channel frequency transfer function H(.omega.) divided by the square-root of the noise spectrum ([N(.omega.)].sup.1/2), and the inputs to summer 305 are flat noise component 302 given by N.sub.o and channel output 303. Then Gallager determines the signal shapes that yield the least lost energy in transmission through the equivalent channel of FIG. 3. These optimum input signals form an orthogonal set that is complete in a restricted sense on the space of bounded energy signals at the channel input. Since the optimum input signals are the eigenfunctions of a singular value decomposition of the channel impulse response, the output signals are also orthogonal. Thus, the result of Gallager offered the tractable feature that the complex channel of FIG. 1 could be decomposed into an array of parallel scalar channels as illustrated in FIG. 4.
In FIG. 4, a.sub.i (e.g., 401,402) is the coefficient in the series expansion in the input signals {.theta..sub.i (t)} that lose least energy on transmission through the equivalent channel 301: ##EQU1## where {.theta..sub.i i(;)} are normalized to have unit energy. With this input, the channel output, s.sub.o (;), is given by ##EQU2## where .lambda..sub.i.sup.1/2 .psi..sub.i (;) is the channel output when the channel input is .theta..sub.i (;). The functions {.psi..sub.i (;)} are normalized to have unit energy by using the normalization constant .lambda..sub.i, which is the channel gain (.lambda..sub.i =energy out/energy in) when .theta..sub.i (;) is transmitted. A receiver matched to recover s(;) would equalize s.sub.o (;) to eliminate the .lambda..sub.i.sup.1/2 factors. This would have the effect of producing noise in the coefficients of the final output (e.g. 407,408 from summers 405 and 406, respectively) that are proportional to ##EQU3## (e.g., 403,404) where N.sub.o is the flattened noise power spectral density.
In a separate study as presented in "The optimum combination of block codes and receivers for arbitrary channels," authored by the present inventor J. W. Lechleider and published in the IEEE Trans. Commun., vol. 38, no. 5, May, 1990, pp. 615-621, Lechleider investigates transmission of short sequences of amplitude modulated pulses through a dispersive channel with colored, added noise. Lechleider found that the channel input sequences that led to the maximum ratio of mean output signal power to mean noise power are the solutions to a matrix eigenvalue problem similar to the integral equation eigenvalue problem considered by Gallager. The structure of this channel is much like a finite dimensional version of FIG. 4. Because of the ubiquity of the form of FIG. 4, the idea of signaling so that the transmission model is a set of parallel, uncoupled subchannels with uncorrelated subchannel noises has come to be known as "Structured Channel Signaling," or SCS. Thus, SCS decomposes a complex vector channel into an ordered sequence of scalar sub-channels with uncorrelated sub-channel noise scalars. Because of this lack of correlation, no noise cancellation techniques can be used to further improve the signal-to-noise performance of the total channel. This places an upper bound on what can be achieved by noise cancellation techniques in SCS.
As discussed by Widrow et al. in the paper "Adaptive noise cancelling: Principles and applications," Proc. IEEE, vol. 63, no. 12, pp 1692-1716, December, 1975, auxiliary measurements are made of noise that are correlated with the noise vector that is received with the signal in order to effect noise cancellation. The correlation is used to form a best estimate of the added noise that is subtracted from the received, noise corrupted signal. But, because of the formulation of SCS, SCS obviates any putative noise-cancellation improvement.
As alluded to in the foregoing background, SCS is a modeling technique for dispersive channels that provides insight into channel performance. Moreover, SCS may also be used as a basis for the design of communication systems. By spreading signals over time and frequency, SCS offers some immunity to structured noise such as impulse noise and narrow-band noise. SCS also offers selective use of the best performing sub-channels for the most important subset of information to be transmitted. SCS subsumes generalized noise cancellation, which is a technique for exploiting the correlation of two different components of noise to reduce the expected noise power of one of the components.
The art is devoid of teachings or suggestions, however, of a methodology and concomitant circuitry for generalized noise cancellation in a communication channel having correlated noise components.